java.util
Class Random

java.lang.Object
  |
  +--java.util.Random

Direct Known Subclasses:

SecureRandom

public class Random

extends Object

implements Serializable

An instance of this class is used to generate a stream of pseudorandom numbers. The class uses a 48-bit seed, which is modified using a linear congruential formula. (See Donald Knuth, The Art of Computer Programming, Volume 2, Section 3.2.1.)

If two instances of Random are created with the same seed, and the same sequence of method calls is made for each, they will generate and return identical sequences of numbers. In order to guarantee this property, particular algorithms are specified for the class Random. Java implementations must use all the algorithms shown here for the class Random, for the sake of absolute portability of Java code. However, subclasses of class Random are permitted to use other algorithms, so long as they adhere to the general contracts for all the methods.

The algorithms implemented by class Random use three state variables, which are protected. They also use a protected utility method that on each invocation can supply up to 32 pseudorandomly generated bits.

Many applications will find the random method in class Math simpler to use.

Since:

JDK1.0

See Also:

Math.random(), Serialized Form

Constructor Summary

Random()
Creates a new random number generator.

Random(long seed)
Creates a new random number generator using a single long seed: public Random(long seed) { setSeed(seed); } Used by method next to hold the state of the pseudorandom number generator.

Method Summary

protected int	next(int bits) Generates the next pseudorandom number.
boolean	nextBoolean() Returns the next pseudorandom, uniformly distributed boolean value from this random number generator's sequence.
void	nextBytes(byte[] bytes) Generates a user specified number of random bytes.
double	nextDouble() Returns the next pseudorandom, uniformly distributed double value between 0.0 and 1.0 from this random number generator's sequence.
float	nextFloat() Returns the next pseudorandom, uniformly distributed float value between 0.0 and 1.0 from this random number generator's sequence.
double	nextGaussian() Returns the next pseudorandom, Gaussian ("normally") distributed double value with mean 0.0 and standard deviation 1.0 from this random number generator's sequence.
int	nextInt() Returns the next pseudorandom, uniformly distributed int value from this random number generator's sequence.
int	nextInt(int n) Returns a pseudorandom, uniformly distributed int value between 0 (inclusive) and the specified value (exclusive), drawn from this random number generator's sequence.
long	nextLong() Returns the next pseudorandom, uniformly distributed long value from this random number generator's sequence.
void	setSeed(long seed) Sets the seed of this random number generator using a single long seed.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Random

public Random()

Creates a new random number generator. Its seed is initialized to a value based on the current time:

 public Random() { this(System.currentTimeMillis()); }

See Also:

System.currentTimeMillis()

Random

public Random(long seed)

Creates a new random number generator using a single long seed:

 public Random(long seed) { setSeed(seed); }

Used by method next to hold the state of the pseudorandom number generator.

Parameters:

seed - the initial seed.

See Also:

setSeed(long)

Method Detail

setSeed

public void setSeed(long seed)

Sets the seed of this random number generator using a single long seed. The general contract of setSeed is that it alters the state of this random number generator object so as to be in exactly the same state as if it had just been created with the argument seed as a seed. The method setSeed is implemented by class Random as follows:

 synchronized public void setSeed(long seed) {
       this.seed = (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1);
       haveNextNextGaussian = false;
 }

The implementation of setSeed by class Random happens to use only 48 bits of the given seed. In general, however, an overriding method may use all 64 bits of the long argument as a seed value.

Parameters:

seed - the initial seed.

next

protected int next(int bits)

Generates the next pseudorandom number. Subclass should override this, as this is used by all other methods.

The general contract of next is that it returns an int value and if the argument bits is between 1 and 32 (inclusive), then that many low-order bits of the returned value will be (approximately) independently chosen bit values, each of which is (approximately) equally likely to be 0 or 1. The method next is implemented by class Random as follows:

 synchronized protected int next(int bits) {
       seed = (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1);
       return (int)(seed >>> (48 - bits));
 }

This is a linear congruential pseudorandom number generator, as defined by D. H. Lehmer and described by Donald E. Knuth in The Art of Computer Programming, Volume 2: Seminumerical Algorithms, section 3.2.1.

Parameters:

bits - random bits

Returns:

the next pseudorandom value from this random number generator's sequence.

Since:

JDK1.1

nextBytes

public void nextBytes(byte[] bytes)

Generates a user specified number of random bytes.

Since:

JDK1.1

nextInt

public int nextInt()

Returns the next pseudorandom, uniformly distributed int value from this random number generator's sequence. The general contract of nextInt is that one int value is pseudorandomly generated and returned. All 2³² possible int values are produced with (approximately) equal probability. The method setSeed is implemented by class Random as follows:

 public int nextInt() {  return next(32); }

Returns:

the next pseudorandom, uniformly distributed int value from this random number generator's sequence.

nextInt

public int nextInt(int n)

Returns a pseudorandom, uniformly distributed int value between 0 (inclusive) and the specified value (exclusive), drawn from this random number generator's sequence. The general contract of nextInt is that one int value in the specified range is pseudorandomly generated and returned. All n possible int values are produced with (approximately) equal probability. The method nextInt(int n) is implemented by class Random as follows:

 public int nextInt(int n) {
     if (n<=0)
		throw new IllegalArgumentException("n must be positive");

     if ((n & -n) == n)  // i.e., n is a power of 2
         return (int)((n * (long)next(31)) >> 31);

     int bits, val;
     do {
         bits = next(31);
         val = bits % n;
     } while(bits - val + (n-1) < 0);
     return val;
 }
 

The hedge "approximately" is used in the foregoing description only because the next method is only approximately an unbiased source of independently chosen bits. If it were a perfect source of randomly chosen bits, then the algorithm shown would choose int values from the stated range with perfect uniformity.

The algorithm is slightly tricky. It rejects values that would result in an uneven distribution (due to the fact that 2^31 is not divisible by n). The probability of a value being rejected depends on n. The worst case is n=2^30+1, for which the probability of a reject is 1/2, and the expected number of iterations before the loop terminates is 2.

The algorithm treats the case where n is a power of two specially: it returns the correct number of high-order bits from the underlying pseudo-random number generator. In the absence of special treatment, the correct number of low-order bits would be returned. Linear congruential pseudo-random number generators such as the one implemented by this class are known to have short periods in the sequence of values of their low-order bits. Thus, this special case greatly increases the length of the sequence of values returned by successive calls to this method if n is a small power of two.

Returns:

a pseudorandom, uniformly distributed int value between 0 (inclusive) and n (exclusive).

Throws:

IllegalArgumentException - n is not positive.

Since:

JDK1.2

nextLong

public long nextLong()

Returns the next pseudorandom, uniformly distributed long value from this random number generator's sequence. The general contract of nextLong is that one long value is pseudorandomly generated and returned. All 2⁶⁴ possible long values are produced with (approximately) equal probability. The method setSeed is implemented by class Random as follows:

 public long nextLong() {
       return ((long)next(32) << 32) + next(32);
 }

Returns:

the next pseudorandom, uniformly distributed long value from this random number generator's sequence.

nextBoolean

public boolean nextBoolean()

Returns the next pseudorandom, uniformly distributed boolean value from this random number generator's sequence. The general contract of nextBoolean is that one boolean value is pseudorandomly generated and returned. The values true and false are produced with (approximately) equal probability. The method nextBoolean is implemented by class Random as follows:

 public boolean nextBoolean() {return next(1) != 0;}

Returns:
the next pseudorandom, uniformly distributed
          boolean value from this random number generator's
		sequence.
Since: 
JDK1.2

nextFloat

public float nextFloat()

Returns the next pseudorandom, uniformly distributed float value between 0.0 and 1.0 from this random number generator's sequence.

The general contract of nextFloat is that one float value, chosen (approximately) uniformly from the range 0.0f (inclusive) to 1.0f (exclusive), is pseudorandomly generated and returned. All 2²⁴ possible float values of the form m x 2^-24, where m is a positive integer less than 2²⁴ , are produced with (approximately) equal probability. The method setSeed is implemented by class Random as follows:

 public float nextFloat() {
      return next(24) / ((float)(1 << 24));
 }

The hedge "approximately" is used in the foregoing description only because the next method is only approximately an unbiased source of independently chosen bits. If it were a perfect source or randomly chosen bits, then the algorithm shown would choose float values from the stated range with perfect uniformity.

[In early versions of Java, the result was incorrectly calculated as:

 return next(30) / ((float)(1 << 30));

This might seem to be equivalent, if not better, but in fact it introduced a slight nonuniformity because of the bias in the rounding of floating-point numbers: it was slightly more likely that the low-order bit of the significand would be 0 than that it would be 1.]

Returns:

the next pseudorandom, uniformly distributed float value between 0.0 and 1.0 from this random number generator's sequence.

nextDouble

public double nextDouble()

Returns the next pseudorandom, uniformly distributed double value between 0.0 and 1.0 from this random number generator's sequence.

The general contract of nextDouble is that one double value, chosen (approximately) uniformly from the range 0.0d (inclusive) to 1.0d (exclusive), is pseudorandomly generated and returned. All 2⁵³ possible float values of the form m x 2^-53 , where m is a positive integer less than 2⁵³, are produced with (approximately) equal probability. The method setSeed is implemented by class Random as follows:

 public double nextDouble() {
       return (((long)next(26) << 27) + next(27))
           / (double)(1L << 53);
 }

The hedge "approximately" is used in the foregoing description only because the next method is only approximately an unbiased source of independently chosen bits. If it were a perfect source or randomly chosen bits, then the algorithm shown would choose double values from the stated range with perfect uniformity.

[In early versions of Java, the result was incorrectly calculated as:

  return (((long)next(27) << 27) + next(27))
      / (double)(1L << 54);

This might seem to be equivalent, if not better, but in fact it introduced a large nonuniformity because of the bias in the rounding of floating-point numbers: it was three times as likely that the low-order bit of the significand would be 0 than that it would be 1! This nonuniformity probably doesn't matter much in practice, but we strive for perfection.]

Returns:

the next pseudorandom, uniformly distributed double value between 0.0 and 1.0 from this random number generator's sequence.

nextGaussian

public double nextGaussian()

Returns the next pseudorandom, Gaussian ("normally") distributed double value with mean 0.0 and standard deviation 1.0 from this random number generator's sequence.

The general contract of nextGaussian is that one double value, chosen from (approximately) the usual normal distribution with mean 0.0 and standard deviation 1.0, is pseudorandomly generated and returned. The method setSeed is implemented by class Random as follows:

 synchronized public double nextGaussian() {
    if (haveNextNextGaussian) {
            haveNextNextGaussian = false;
            return nextNextGaussian;
    } else {
            double v1, v2, s;
            do { 
                    v1 = 2 * nextDouble() - 1;   // between -1.0 and 1.0
                    v2 = 2 * nextDouble() - 1;   // between -1.0 and 1.0
                    s = v1 * v1 + v2 * v2;
            } while (s >= 1);
            double norm = Math.sqrt(-2 * Math.log(s)/s);
            nextNextGaussian = v2 * multiplier;
            haveNextNextGaussian = true;
            return v1 * multiplier;
    }
 }

This uses the polar method of G. E. P. Box, M. E. Muller, and G. Marsaglia, as described by Donald E. Knuth in The Art of Computer Programming, Volume 2: Seminumerical Algorithms, section 3.4.1, subsection C, algorithm P. Note that it generates two independent values at the cost of only one call to Math.log and one call to Math.sqrt.

Returns:

the next pseudorandom, Gaussian ("normally") distributed double value with mean 0.0 and standard deviation 1.0 from this random number generator's sequence.